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C. SCHREIBER.

PROTBACTOR. APPLICATION FILED NOV. 6. I916.

Patented Oct. 14, 1919.

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PROTRACTOR. APPLICATION FILED NOV. 6. 1916. 1,318,607. Patented Oct. 14

2 SHE ETSSHEE His A??? UNITED STATES PATENT orrron. A

CONRAD SCHBEIBER, or snnrnnncrsco, CALIFORNIA,

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Specification of Letters I 'atent. Patented Oct. 14, 1919. I

Application. filed No ember 6, 1916; Serial No. 130,909.

To all whom it may concern:

Be it known thatI, CONRADSCHREIBER, a citizen of the United States,residing in the city and county ofSan Francisco and State of California,have invented a new and'use ful Improvement in Protractors, of whichthe'following is a specification.

My invention relates to protractors for the use of" car-penters,f1nillWrights, sheet metal workers and other artisans, whose work requires aknowledge of geometry and trigonometry, and wherein certain 1 angles andlengths of curves must be determined, and the objects of my inventionare First, to provide an improved protractor arranged to indicate in astraight line the length of anarc; Q a

Second, to provide an improved protractor adapted to provide a meanswhereby a circle or any portion thereof may be laid out. withreasonableaccuracy;

Third,.to provide an improved protractor arranged to determine thelength of one side of several polygons capable of being inscribed withinany circle. I

l I accomplish these'several objects by means of the preferred form ofan arc of the device disclosed in the drawings forming a part of thepresent specification wherein like characters of reference are used todesignate similar parts throughout the said specification'and' drawings,and in which 1 Figure 1 is a plan view of one side of the protractor. v

Fig. 2 is a side elevation of Fig. l.

Fig. 3 is a plan view ofthe reverse'or opposite side of the protractor,and

Fig. 4 is a diagrammatic view disclosing I one application of thedevice;

The design and operation of this device is based on the well knownprinciple that when corresponding angles of several triangles are equalthe corresponding sides of the said: triangles are in direct proportionto each other. 1

Referring to the drawings the numeral 1 is used to:designate acomparatively thin and fiat protractor having an arcua-te edge 2 and anopposite straight edge 3,

Both faces or sides of the protractor 1 are graduated radially from the.arcuate edge 2:to indicate degrees, and othergraduations 4' extendfromthe intersections ofsaid de gree graduations with the arcuate edge 2across the faces or surfaces of the protractor 1 to the straight edges 3thereoff The direction of the graduations 4c is such that a lengthbetween the end graduations on the straight edge 3 equalize the lengthofthe arcuate ed e 2 will be divided into the same number of parts as saidarcuate edge 2.

Hence the length, in. astrai'ght line, of an arc of one or any number ofdegrees of the circle represented by-the 'arcuate edge Qnay be instantlydetermined and measured 0..' The actual dimension of each space betweenthe graduations representing one de gree is actually'two degrees inlength, the purpose of which will hereinafter be more fully set forth.

Theface of the'arcuate edge 2 is provided with certain graduations 6which represent the chord of an arc, or one side of various polygons. IGraduations for producing an equilateral triangle, a three-sidedpolygon. as well as graduations for a square or four-sided poly gon, arenotlgiven as these maybe easily Y the angle at C will be 180minus 135 or45.

. Therefore, the sides, 7 are at an angle of 45 relatively to each otherinsteadof22 as indicated by the graduations 4E, and eight of theseprotractors, or thesame protractor turned over on its ends 8 times wouldcompleteacircle andif a line were drawn along the straight edge ateachturn an octagon would be described.

. Itv will be notedIin Fig. 2 that the numeral 6,.as well as certainother, numerals indicat ingthe graduations 6, are inverted. The reasonfor this will be apparent when 1t 1s noted that one sixth is greater inlength than one eighth of a circle. Therefore, to measure offthe'lengthof one side of, a hexagon it would be necessary to lay .theprotractor in-Fig. 4C and then turn, it upon lts upper end 7 whichwouldlay the protractor 1: on the adjacent eighth of the clrcleand turn baseline G. One-fifth of a circle would be longer and is indicated fartheron. The numeral or index 8 is also indicated midway between the ends ofthe arcuate edge 2 and from this it is apparent that an octagon may belaid out from two points, viz; the center as well as from the ends ofthe protractor 1.

In laying out the sides of a hollow octagonal column it is evident thatboards of the proper width have longitudinal edges beveled to an angleof 22 from the edges of the board. Therefore, I find from experimentthat it is more convenient to designate the included are on the arcuatesides 2 as being 22% instead of 15 which is the actual degree. A furtherreason for indicating the degrees as twice the actual size is that inlaying out longitudinal boards for hollow octagonal, hexagonal or otherpolygons, that the amount of material to be beveled off from the edge ofthe board is equivalent to a wedge including an angle of a degreeindicated by the width of the board on the arcuate edge 2 of theprotractor 1.

This is evident in laying out an octagonal hollow column composed ofboards to form the longitudinal sides of the column.

Referring to Fig. 4 consider the protractor 1 as being a cross sectionof one of the longitudinal boards or members comprising a hollowoctagonal column.

It will be observed that seven other boards similar in cross sectionlaid edge to edge would form an octagonal column and that to bevel theedges of said boards to make them fit it would be necessary to remove awedge from both edges of each board equal to an angle of 22%; which isthe degree of the are indicated by the protractor 1 or the arcuate edge2 thereof. Were the members made of solid wedges instead of fiat boardssaid wedges would include angles of 45 each, eight of them beingrequired to form an octagonal column.

It will be found that this is true of other required polygons. Informing a hexagonal column there would be six wedges, each including anangle of 30. To find the proper bevel for the edges of six boards tomake them form a hollow hexagonal column the protractor 1 would be firstlaid as indicated in full lines in Fig. 4; of the drawings and thenturned over on its upper edge so that the protractor 1 would be reversedor inverted and occupy the adjacent section or eighth of the circle ofwhich the arcuate edge is a portion.

The index 6 on the arcuate surface 2 would then be found opposite theradial graduation indicated by the index 30, or at 30 as marked on. thearcuate edge 2 of the protractor 1. This would indicate. 6 sides to bebeveled at an angle of 30 from each edge of each board.

It is obvious from the foregoing that the number of sides required ordesired may be obtained and simultaneously the degree each board is tobe beveled from the sides thereof will be indicated by the degrees onthe arcuate edge 2.

As shown in Fig. 1 the ends of the plate are inclined at an angle of67:} degrees from the back or straight edge of the plate and the face ofthe plate is provided with an index numeral 22;- degrees meaning thedegree of angle of the edge from a line which is perpendicular to theplane of the face of the board and which indicates accurately the bevelat the edge of the board necessary 111 matching boards to form anoctagonal column the included angle of each segment being 45 degrees ofwhich the degree angle or ends of the protractor is one-half.

A further use and advantage of the protractor 1 may be as follows:

I The protractor may be used to determine the length of a side of anypolygon of adiameter other than that of the protractor.

To determine the length, in a straight line, for cornice or sheet metalwork as well as for carpentry, of any portion of a circle of any radiusor diameter or any chord, the protractor 1 is laid down as indicated inFig. 1 of the drawings.

The present protractor has for an arcuate edge a portion of a circlestruck with a twelve-inch radius. If it is desired to find the length ofone side of a polygon inscribed within'a' circle of six-inch radius theprotractor 1 is first laid on the plot in the position indicated indotted lines in Fig. 1 of the drawings and a chord A equal in length to,let us say, an arc of twenty degrees of a twelve-inch radius, is markedoff on an arc corresponding to the arcuate edge 2 of the protractor 1. Aradius B is then drawn from the upper end of the chord A to the center Cof the circleof which the arcuate edge 2 is a portion.

An are D, of the required radius is then produced and the chord E of theare D is the required length of a piece of material which will producean arc of twenty degrees on the required radius which may be greater orlesser than the radius of the edge 2.

This is evident from the principle that triangles having similarcorresponding angles have similar sides and are in direct proportion toeach other, and the angle included between the base line G and theradius B is similar in both triangles produced.

Any side of a given polygon inscribed in circles of different diametersmay be obtained in a similar manner.

It is obvious from the foregoing that I have provided an improvedprotractor wherein the length in a straight line of any portion of anarc may be determined as well as the length of one side of any polygon.

Having thus described my invention what I claim as new and desire tosecure by Letters Patent is 1. A protractor having a graduated arcuateedge and an opposite straight edge graduated to give the length inastraight line of a' corresponding portion of the arcuate edge.

2. A protractor having an arcuate edge and means on the said edge forindicating the length of one side of various polygons inscribed Withinany circle.

3. A protractor having an arcuate edge and an opposite straight edge andgraduations on both sides of the protractor dividing the arcuate andstraight edges into spaces of equal length, the graduations on one facebeing numbered successively with the graduations on the opposite face.

A protractor having an arcuate edge and an opposite straight edge andgraduspaces of equal length.

5. A protractor having an arcuate edge graduated with degree marks andindices,

coordinate to the degree marks, on the faceof the arcuate edge forindicating the length of one side of several polygons.

6. A protractor having a graduated arcuate edge and an opposite straightedge graduated to indicate the length in a straight line of any portionof the arcuate edge, the ends of said protractor being arranged radialto the arcuate edge and 67% degrees to the straight edge.

In Witness whereof I hereunto set my signature. I

CONRAD SOHREIBER.

Copies of this patent may be obtained for five cents each, by addressingthe Commissioner of Patents, Washington, D. G.

